Question

Part A

A current flows in a plane rectangular current loop
withheight and horizontal sides . The loop is placed into a uniform
magneticfield in such a way that the sides
oflength are perpendicular to , andthere is
an angle between the sides of
length and .

Calculate , the magnitude of the torque about
thevertical axis of the current loop due to the interaction of
thecurrent through the loop with the magnetic field.

Express the magnitude of the torquein
terms of the given variables. You will need a trigonomericfunction
[e.g., or ]. Use for the magnitude of the magnetic
field.

Part C
A current flows around a plane circular loop of
radius, giving the loop a magnetic
dipolemoment of magnitude . The loop is placed in a uniform magnetic
field, with an angle between the direction of the field
linesand the magnetic dipole moment as shown in the figure.
Find
anexpression for the magnitude of the torque on the current loop.

Express the torque explicitly interms
of , , , , and (where and are the magnitudes of the respective
vectorquantities). Do not use . You will need a trigonomeric function
[e.g.. or ].